International Journal of Mathematics and Mathematical Sciences
Volume 14 (1991), Issue 1, Pages 27-44
doi:10.1155/S0161171291000030

Some properties of the functional equation ϕ(x)=f(x)+∫0λxg(x,y,ϕ(y))dy

Abstract

A discussion is given of some of the properties of the functional Volterra Integral equation ϕ(x)=f(x)+∫0λxg(x,y,ϕ(y))dy. and of the corresponding multidimensional equation. Sufficient conditions are given for the uniqueness of the solution, and an iterational process is provided for the construction of the solution, together with error estimates. In addition bounds are provided on the solution. The results obtained are illustrated by means of the pantograph equation.